Dipole sums on a surface with fractional coverage: Application to enhanced Raman spectra of halide ions on silver

A procedure is developed for calculating the dipole sum for a lattice of sites in which not all sites are occupied. The summation accounts for molecules far from the origin as well as for statistical fluctuations in site occupancy near the origin. Vibrational frequencies are then calculated at various coverage fractions for chloride ions adsorbed on silver (100) in which a dipolar interaction potential is used to couple individual Cl–Ag vibrational modes. One vibrational frequency is calculated for each particular distribution of Cl− ions. This process is repeated for a large number of distributions having the same coverage fraction and the relative occurrence of the frequencies are then displayed as a histogram. Calculated histograms at low coverage exhibit structural features characteristic of the number of nearest neighbors to the origin ion. These structural features agree qualitatively with recent experimental observations.